Some subclasses of analytic functions of complex order

Abstract

In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient conditions for the functions belonging to these classes are also given. Moreover, coefficient bound estimates for the functions belonging to these classes are obtained.

Analytic Function of Complex Order Involving Certain Multiplier Transform

“…Remark 2.3. This result agrees with the Corollary 2.1 in [7] and Corollary 6 in [5] with δ = γ . Corollary 2.8.…”

“…In this study, we apply the generalized multiplier transform of Makinde et-al [4], in the method of Mustafa [7]. The results in this paper generalize the work of Irmak et.…”

“…The classes S * (δ) and C(δ) are the special cases of the unification for τ = 0, 1 respectively. Moreover, Altintas et al and other researchers studied the class T S * C(δ, τ ) see [3,5,6] and using the unification in (1.2), Nizami Mustafa [7] introduced and investigated the classes S * C(δ, τ ; η) and T S * C(δ, τ ; η), 0 ≥ δ < 1; τ ∈ [0, 1]; η ∈ C which he defined as follows:…”

“…where k ∈ N. Motivated by the work of Mustafa, Makinde and Najafzadeh in [7,4], we study effect of the application of the linear operator D s α,β,γ f on the unification of the classes of the functions S * C(γ, β; τ ). Now, we define S * C(δ, µ, α, γ, β; b) to be class of functions f ∈ S satisfying the condition…”